Artificial Intelligence CS 344 Artificial Intelligence By Prof: Pushpak Bhattacharya Class on 25/Jan/2007

Logic and inferencing Vision NLP Search Reasoning Learning Knowledge Robotics Expert Systems Planning Obtaining implication of given facts and rules -- Hallmark of intelligence

Inferencing through Deduction Induction Deduction (General to specific) Induction (Specific to General) Abduction (Conclusion to hypothesis in absence of any other evidence to contrary) Deduction Given: All men are mortal (rule) Shakespeare is a man (fact) To prove: Shakespeare is mortal (inference) Induction Given: Shakespeare is mortal Newton is mortal (Observation) Dijkstra is mortal To prove: All men are mortal (Generalization)

If there is rain, then there will be no picnic Fact1: There was rain Conclude: There was no picnic Deduction Fact2: There was no picnic Conclude: There was no rain (?) Induction and abduction are fallible forms of reasoning. Their conclusions are susceptible to retraction Two systems of logic 1) Propositional calculus 2) Predicate calculus

Propositions Stand for facts/assertions Declarative statements As opposed to interrogative statements (questions) or imperative statements (request, order) Operators => and ¬ form a minimal set (can express other operations) - Prove it. Tautologies are formulae whose truth value is always T, whatever the assignment is

Model In propositional calculus any formula with n propositions has 2n models (assignments) - Tautologies evaluate to T in all models. Examples: 1) 2) - De Morgan with AND

Semantic Tree/Tableau method of proving tautology To prove: Start with the negation of the formula to be proved a tautology α-formula β-formula - β - formula α-formula - α - formula

Example 2: Contradictions in all paths X (α - formula) (α - formulae) B C Contradictions in all paths B C

Exercise: Prove the backward implication in the previous example